Am doing some problems on complex analysis and am having some trouble getting my head around some of the basic points.

If z represents a point R on the complex plane,

and I take i . z to give another point T , then the line segment OT will be perpendicular to OR.

to show this is true is the following correct?

z = x +yi =$\displaystyle r.e^{(i.\theta)}$

and i.z = $\displaystyle 1.e^{(i.(\pi/2))} . r.e^{(i.\theta)}$

therefore = $\displaystyle r.e^{i(\theta + \pi/2)}$

and as the argument here has been shifted by pi/2 the second point is perpendicular from the first?